Is high sensitivity always desirable for a grating-based differential phase contrast imaging system?

Abstract

In grating-based x-ray differential phase contrast (DPC) imaging, the measured signal amplitude of the phase shift induced by an image object is proportional to the so-called system sensitivity. Therefore, to achieve a better signal-to-noise (SNR) for improved imaging performance, it is generally believed that one should increase the system sensitivity by reducing the period of the analyzer grating or increasing the distance between the phase grating and analyzer grating. The purpose of this work is to theoretically and experimentally demonstrate that there is an optimal system sensitivity to attain the highest SNR for a given task provided that the standard phase-stepping acquisition and phase retrieval methods are used. When system sensitivity goes beyond this optimal value, SNR decreases and the imaging performance deteriorates. Due to the fundamental fact that the measured phase signal is a cyclic variable, the phase wrapping effect is inevitable in DPC imaging when the system sensitivity increases. The phase wrapping effect appears in both signal and noise measurements. The effect in the signal measurement is manifested in the so-called signal statistical bias and such effect often impacts the accuracy of the measurement. The phase wrapping effect also appears in the noise variance measurement and impacts the precision of the measurement. A thorough theoretical analysis was performed in this work to demonstrate the quantitative impacts of phase wrapping on both signal bias and noise variance and thus on the actual system SNR. The joint effect of phase wrapping in both the signal bias and noise variance yields an optimal system sensitivity to achieve the highest SNR. Both extensive numerical simulation studies and experimental studies were performed to validate the theoretical analysis. Both theoretical analysis and experimental studies show that the SNR of the DPC signal is not always proportional to the sensitivity due to the cyclic nature of the signal and the phase wrapping effect. For a given refraction angle and exposure level, there exists an optimal sensitivity factor that maximizes the SNR, beyond which, increasing the sensitivity will decrease the SNR. Increase of system sensitivity does not always improve x-ray DPC imaging performance provided that the standard phase-stepping acquisition and phase retrieval methods are used.